An adiabatic cylinder has 8 gram of helium in it at 400 K and its piston of area $1 c m^{2}$ (which has mass 1 kg) is movable. If a block of mass 62 kg is placed on the piston then the final temperature of the gas will be $(n \times 100) K$ find the value of $n$ (Take atmospheric pressure to be $10^{5} N m^{- 2}$ and $g = 10 m / s^{2}$ )

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Detailed Solution

$P_{1} = P_{0} = 10^{5} P a + \frac{1 \times 10}{10^{- 4}} = 2 \times 10^{5} P a; P_{2} = P_{0} + \frac{M g}{A} = 10^{5} + \frac{63 \times 10}{10^{- 4}} = 64 \times 10^{5} P a$

For adiabatic process $\frac{T_{1}^{γ}}{P_{1}^{γ - 1}} = \frac{T_{2}^{γ}}{P_{2}^{γ - 1}}, \frac{{(400)}^{\frac{5}{3}}}{{(2 \times 10^{5})}^{\frac{2}{3}}} = \frac{T_{2}^{\frac{5}{3}}}{{(64 \times 10^{5})}^{\frac{2}{3}}}$

$T_{2} = 400 {(32)}^{\frac{2}{5}} = 400 \times 2^{2} = 1600 K$

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